Comparing and Scaling
Tasnim Mostafa
Math 7D
Scaling Up or Down
Investigation 6
Problem 6.1
BIG IDEA:
Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
Investigation 6 Essential Question:
Which comparing strategies work best in which situations?
Notes: To make things larger or smaller you can use a scale factor.
Lager then Average Human (average count)
Weight: 90 kilograms
Height: 2 meters
Skull length: 20 centimeters
Incisors length: 1 centimeter
How big was T. rex compared to a “larger than average” human being? The T.rex was MUCH bigger then a “larger than average” human being. Everything that was measured of a T.rex was bigger then everything measured for a “larger than average” human.
T. rex weighed 8010 kilograms more than a “larger than average” human
90kg >human weight, x 90 equals 8100kg < T-Rex Weight
T. rex was 4 meters taller than a “larger than average” human
2m> human height, x 3 equals 6m <Rex Height
T. rex’s skull was 80 centimeters longer then a “larger than average” human
20cm >human skull length x 5 equals 1m <Rex Skull lengths.
T.rex’s incisors were 14 centimeters longer then a “larger than average” human
1cm <human incisor length x 15 equals 15cm >Rex Incisor length.
So basically the T.rexes were/had
90 times heavier than a “larger than average” human.
3 times taller than a “larger than average” human.
5 times bigger skulls then a “larger than average” human’s skull
15 times larger teeth then a “larger than average” human’s teeth.
Write a paragraph to help someone younger then you understand how the size of T.rex compares to the size of a human. Be specific about the comparisons you are making.
Some of our favorite stories have to do with Dinosaurs and how they lived on our earth a long, long time ago. We know that Dinosaurs were big from what we’ve heard but wouldn’t we like to know exactly how big? Well no problem we can know now. Archeologists (people who study old things and history) dug up various parts of a dinosaur’s body. Not just any dinosaur but a special one. His name is T.rex, he was a very big guy. Now imagine a pretty big human guy like your dad but slightly bigger. So this T.rex dinosaur was 3 times his height. So if you stacked up 3 of those big humans you would be able to see how tall T.rex was. The T.rex also weighed a lot! About 8100 kilograms! We’re talking like 6 really fat people combined. Of course to weigh so much they must have ate a lot of different things and to help them do that they had huge teeth (called incisors). Their teeth were about 14 times a big human tooth. To be able to have these teeth the T.rex had a big head/skull too. His skull was 80 centimeters more then a big human skull. So now we know that dinosaurs especially T.rex’s were really big! And since they were so much bigger then humans they could have harmed us if they were still around. But luckily there not. So we have nothing to worry about.
Follow up:
1. Suppose an infant T. rex was the same height as the “larger than average” human described in the problem above, but he was still similar to an adult T.rex. What would be the scale factor between a grown T. rex and the infant T.rex?
The infants height is same as “larger than average” and the T.rex is three times that height. So the scale factor would be 1/3
2. How long were the incisors of this young T.rex? Grown T-Rex’s incisors= 15cm Scale Factor=1/3 1/3 of 15cm=5cm
Incisors were 5 cm
3. How long was the skull of this young T.rex?
Grown T-Rex’s skull=1 meter Scale Factor=1/3 1/3 of a meter=33cm Skull is 33 cm
Vocab words: Population Density- measurement of population per unit area Rate- frequency relative to a time unit Ratio- relative magnitudes of two quantities Scale, Scaling- scale is an ordered reference standard, scaling is the act of arranging in a graduated series Unit Rate- A rate with the second term being one unit Decimal- A linear array of digits that represents a real number Difference- the quality of being unlike or dissimilar Equation-a mathematical statement that two expressions are equal Equivalent ratio-two ratios that have the same value Fraction- a component of a mixture Graph, Coordinate graph- chart the data ,grid with x and y axes crossing through the center Percent- a proportion in relation to a whole Scale Factor- A number which scales or multiplies some quantity Proportion-the quotient obtained when the magnitude of a part is divided by the magnitude of the whole
Tasnim Mostafa
Math 7D
Scaling Up or Down
Investigation 6
Problem 6.1
BIG IDEA:
Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
Investigation 6 Essential Question:
Which comparing strategies work best in which situations?
Notes:
To make things larger or smaller you can use a scale factor.
Problem 6.1
T.rex (average count)
Weight: 8100 kilograms
Height: 6 meters
Skull length: 1 meter
Incisors length: 15 centimeters
Lager then Average Human (average count)
Weight: 90 kilograms
Height: 2 meters
Skull length: 20 centimeters
Incisors length: 1 centimeter
How big was T. rex compared to a “larger than average” human being?
The T.rex was MUCH bigger then a “larger than average” human being. Everything that was measured of a T.rex was bigger then everything measured for a “larger than average” human.
T. rex weighed 8010 kilograms more than a “larger than average” human
90kg >human weight, x 90 equals 8100kg < T-Rex Weight
T. rex was 4 meters taller than a “larger than average” human
2m> human height, x 3 equals 6m <Rex Height
T. rex’s skull was 80 centimeters longer then a “larger than average” human
20cm >human skull length x 5 equals 1m <Rex Skull lengths.
T.rex’s incisors were 14 centimeters longer then a “larger than average” human
1cm <human incisor length x 15 equals 15cm >Rex Incisor length.
So basically the T.rexes were/had
90 times heavier than a “larger than average” human.
3 times taller than a “larger than average” human.
5 times bigger skulls then a “larger than average” human’s skull
15 times larger teeth then a “larger than average” human’s teeth.
Write a paragraph to help someone younger then you understand how the size of T.rex compares to the size of a human. Be specific about the comparisons you are making.
Some of our favorite stories have to do with Dinosaurs and how they lived on our earth a long, long time ago. We know that Dinosaurs were big from what we’ve heard but wouldn’t we like to know exactly how big? Well no problem we can know now. Archeologists (people who study old things and history) dug up various parts of a dinosaur’s body. Not just any dinosaur but a special one. His name is T.rex, he was a very big guy. Now imagine a pretty big human guy like your dad but slightly bigger. So this T.rex dinosaur was 3 times his height. So if you stacked up 3 of those big humans you would be able to see how tall T.rex was. The T.rex also weighed a lot! About 8100 kilograms! We’re talking like 6 really fat people combined. Of course to weigh so much they must have ate a lot of different things and to help them do that they had huge teeth (called incisors). Their teeth were about 14 times a big human tooth. To be able to have these teeth the T.rex had a big head/skull too. His skull was 80 centimeters more then a big human skull. So now we know that dinosaurs especially T.rex’s were really big! And since they were so much bigger then humans they could have harmed us if they were still around. But luckily there not. So we have nothing to worry about.
Follow up:
1. Suppose an infant T. rex was the same height as the “larger than average” human described in the problem above, but he was still similar to an adult T.rex. What would be the scale factor between a grown T. rex and the infant T.rex?
The infants height is same as “larger than average” and the T.rex is three times that height. So the scale factor would be 1/3
2. How long were the incisors of this young T.rex?
Grown T-Rex’s incisors= 15cm
Scale Factor=1/3
1/3 of 15cm=5cm
Incisors were 5 cm
3. How long was the skull of this young T.rex?
Grown T-Rex’s skull=1 meter
Scale Factor=1/3
1/3 of a meter=33cm
Skull is 33 cm
Vocab words:
Population Density- measurement of population per unit area
Rate- frequency relative to a time unit
Ratio- relative magnitudes of two quantities
Scale, Scaling- scale is an ordered reference standard, scaling is the act of arranging in a graduated series
Unit Rate- A rate with the second term being one unit
Decimal- A linear array of digits that represents a real number
Difference- the quality of being unlike or dissimilar
Equation- a mathematical statement that two expressions are equal
Equivalent ratio-two ratios that have the same value
Fraction- a component of a mixture
Graph, Coordinate graph- chart the data ,grid with x and y axes crossing through the center
Percent- a proportion in relation to a whole
Scale Factor- A number which scales or multiplies some quantity
Proportion- the quotient obtained when the magnitude of a part is divided by the magnitude of the whole